Solve the Differential Equation $y ^ { tt } - 6 y ^ { t} + 5 y = 20 x \text { by the method of undetermined }$

question 3

Multiple Choice

Solve the differential equation $y ^ { tt } - 6 y ^ { t} + 5 y = 20 x \text { by the method of undetermined }$ coefficients.

• A)\(y = C _ { 1 } e ^ { 9 x } + C _ { 2 } e ^ { 5 x } + 4 x - \frac { 24 } { 5 }\)
• B)\(y = C _ { 1 } e ^ { 9 x } + C _ { 2 } e ^ { 7 x } + 4 x - \frac { 24 } { 5 }\)
• C)\(y = C _ { 1 } e ^ { x } + C _ { 2 } e ^ { 7 x } + 4 x - \frac { 24 } { 5 }\)
• D)\(y = C _ { 1 } e ^ { x } + C _ { 2 } e ^ { 5 x } + 4 x + \frac { 24 } { 5 }\)
• E)\(y = C _ { 1 } e ^ { 9 x } + C _ { 2 } e ^ { 7 x } + 4 x + \frac { 24 } { 5 }\)

---

Definitions:

Experimental Method

A research method involving the manipulation of variables to determine cause and effect relationships.

Ethical Limitations

Boundaries set by moral principles that guide individuals' actions and decisions, particularly in professional contexts.

Psychological Research

The systematic investigation of mental processes and behavior through experiments, observation, and analysis.

Safeguards

Measures or mechanisms put in place to protect against unforeseen harm, error, or violation in various contexts.